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AP EAMCET202316 May 2023Morning ShiftMathematicsHyperbolaActual

7. If is the angle between the asymptotes of the hyperbola x^2 a^2 - (y-2)^2 4 =1 and = 5 13 , then a^2=

Options

  1. A16 3 or 18
  2. B16 9 or 9
  3. C16 7 or 6
  4. D16 5 or 11

Correct answer

B. 16 9 or 9

Step-by-step solution

Eqn. of hyperbola is x^2 a^2 - (y-2)^2 4 =1 and = 5 13 = 12 5 ...(i) Angle between the asymptotes of hyperbola is = ⁻¹ ( 2 2 a a^2-4 ) ( )= 4 a a^2-4 ...(ii) From eqns. (i) and (ii) aligned & 12 5 = 4 a a^2-4 3 a^2-5 a-12=0 & (a-3)(3 a+4)=0 & a=- 4 3 , 3 a^2= 16 9 , 9 . aligned

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